Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 5 - Section 5.4 - The Pythagorean Theorem - Exercises - Page 253: 34

Answer

If $a^2+b^2 \ne c^2$, then the triangle is not a right triangle.

Work Step by Step

We know from given theorems that if $a^2 + b^2 < c^2$, then the triangle is obtuse and that if $a^2 + b^2 > c^2$, then the triangle is acute. The only other triangle is a right triangle, and the only other formula is $a^2 + b^2 = c^2$. Thus, a triangle is right if and only if $a^2 + b^2 = c^2$. Thus, if $a^2+b^2 \ne c^2$, then the triangle is not a right triangle.
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